26) The area of the parallelogram having a diagonal 3 i + j - k and a side i - 3 j + 4 k   i s  
(1) 10 3
(2) 6 30
(3) 3 2 30
(4) 3 30

Dear Student,

Let ABCD be the parallelogram and AC be its one of the diagonal.Let, AC = 3i^ + j^ - k^Let AB = i^ -3j^ +4k^Now, AB + BC = AC     Parallelogram law of vector additionBC = AC - ABBC = 3i^ + j^ - k^ - i^ -3j^ +4k^ = 2i^ +4j^ - 5k^Now, AB × BC = i^j^k^1-3424-5=i^15-16 - j^-5-8 + k^4+6=-i^ + 13j^ + 10k^Now, area of paralleogram ABCD = AB × BC = -12 + 132 + 102 = 270 = 330

Regards

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